$1/N$ expansion: Calculation of anomalous dimensions and mixing matrices in the order $1/N$ for $N\times p$ matrix gauge-invariant $\sigma$-model

In the first order in $1/N$ for arbitrary dimension $2<d<4$ of space the following quantities are calculated for the $N\times p$ matrix $\sigma$ model [1] quantized by means of auxiliary scalar ($\varphi$) and vector ($B_\mu$) matrix fields: 1) the anomalous dimensions of all the fields; 2) the matrix of the anomalous dimensions of the mixed operators $\varphi$ and $B^2$ of the canonical dimension 2; 3) the matrix of the anomalous dimensions of the four mixed gauge-invariant composite operators of the type $\varphi^2$ and $G_{\mu \nu}G_{\mu \nu}$ of canonical dimension 4 determining four critical exponents $\omega$.